Article by SP3L Modeling Various Configurations of Capacitance-Hat Dipoles

I modeled a number of shortened dipoles with various capacitive hats at their ends. I think the results may interest you.

All models had 2.5 m (8.2 ft.) long main element with a feed point in its center. 2.5 m is about 1/8 wavelength in 20 m band. The mini dipoles differed in the type of hats connected to their ends. Majority hats (but not all) were designed with cross shaped spreaders in mind. So, the supporting structure in most cases would look like in the sketch below.

The views and performance parameters of all models are presented in the tables below.

* included for reference only
** SWR calculated for 50 ohm source

In most cases, there is only small penalty in gain w.r.t. full length ½ lambda dipole (-0.7 … -0.5 dBd). The gain remains practically constant over the whole band.
The radiation pattern of a mini dipole is practically identical with the ½ lambda dipole. Have a look at the total gain 3-D plot:

All models have resonance resistance close to 12.5 ohm what make them relatively easy to match to 50 ohm coaxial cable. 1:4 balun like that in the Cobweb can be used for the purpose.

On the other hand, there are significant differences in bandwidth among the models. Probably the most popular shapes are the Checkbox and 1-Arm Spiral. The first has quite wide bandwidth but the latter is rather poor solution. You can notice improvement with the 2-Arm Spiral but the 4- Arm Spiral is even better. I would not recommend building 1-Arm Spiral version.

Triangle No. 1 and No. 2 can be of interest of those who would like to hide their mini dipole under a roof. The mini dipole with Triangle No. 2 hats can be build on two vertical poles assuming 4 strings are added to anchor the lower ends of wires (it will look like a tent).

I also checked if adding inductors can reduce the size of hats. And yes, the size is reduced but at the cost of bandwidth. Slightly better results can be achieved if the inductors are mounted closer to the feed point rather than closer to the hats. However, I doubt if the improvement in size is worth the effort of adding the inductors.

To compare the 1/8 lambda mini dipole with other solutions, I added to the comparison: a broken square loop (single band version of the Cobweb) and bent ends dipole. The broken square loop has dimensions: 2.6 x 2.6 m.

1/12 lambda mini dipole

I simulated also shorter dipoles: 1/12 lambda long. Their resonance resistance dropped to about 5.6 ohm what is 1/9 of 50 ohm. The simulation results are shown in the table below.

1/12 lambda dipoles have narrower bandwidth. Some hats are no longer suitable due to narrow bandwidth. The hats that still can be used (like the Checkbox) are rather big when compared with antenna length. In my opinion, 1/12 lambda dipoles are not practical.

Generally, when you shorten a full size dipole and add capacitance hats at its ends to maintain resonance at the same frequency, following things happen:
1) resonance resistance decreases,
2) required size of the hats increases,
3) bandwidth decreases,
4) gain decreases.

1/8 lambda seems to be a good choice for a shortened dipoles because:
1) resonance resistance is close to ¼ x 50 ohm what makes it easy to match to a coaxial cable,
2) size of the hats is in good proportion to the antenna length,
3) decrease in gain is small,
4) if the hat type is properly chosen, bandwidth is sufficient for 40-12 m bands; half of the 10 m band or slightly more can be covered; about 100 kHz of 80 m band can be covered (although I am not sure if the antenna would be practical for this band).

Let me know if you are interested in this topic. I did more research and can share more information if there is interest in it. I can also share the NEC models if you want them.